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Durango Bill's

Bingo Probabilities



Bingo Probability Statistics Analysis
Data for Picture Frame (All 4 edges) and the Letter "Y"

   The 2nd column in the table below shows the single-board probability that all four edges will be filled when the "Nth" number is called. The 3rd column shows the cumulative single-board probability that all four edges will be filled on or before the "Nth" number is called.

   The 4th and 5th columns in the table show similar data, but for a large "Y" (Upper left to center, upper right to center, center to middle cell on the bottom row)

If we look at the table below we see that when the 20th number is called in a Bingo game, we get the following probabilities.

1) A single board has a 4.53331E-13 probability of filling all 4 edges when the 20th number is called.
2) A single board has a 5.66664E-13 probability of filling all 4 edges on or before 20 numbers are called.
3) A single board has a 5.77474E-05 probability of completing a "Y" when the 20th number is called.
4) A single board has a 0.000192491 probability of completing a "Y" on or before the 20th number is called.

Computer program and data by Bill Butler

Quantity    All 4 Edges     Cumulative      Letter Y        Cumulative
of Bingo    Probability     Probability     Probability     Probability
Numbers     This Turn       All 4 Edges     This Turn       Letter Y
Picked      1 Board         1 Board         1 Board         1 Board
-----------------------------------------------------------------------
     1      0               0               0               0
     2      0               0               0               0
     3      0               0               0               0
     4      0               0               0               0
     5      0               0               0               0
     6      0               0               4.96624E-09     4.96624E-09
     7      0               0               2.97974E-08     3.47637E-08
     8      0               0               1.04291E-07     1.39055E-07
     9      0               0               2.78109E-07     4.17164E-07
    10      0               0               6.25746E-07     1.04291E-06
    11      0               0               1.25149E-06     2.2944E-06
    12      0               0               2.2944E-06      4.58881E-06
    13      0               0               3.93326E-06     8.52207E-06
    14      0               0               6.39155E-06     1.49136E-05
    15      0               0               9.94241E-06     2.4856E-05
    16      1.16958E-16     1.16958E-16     1.49136E-05     3.97697E-05
    17      1.87133E-15     1.98829E-15     2.16925E-05     6.14622E-05
    18      1.59063E-14     1.78946E-14     3.07311E-05     9.21933E-05
    19      9.54381E-14     1.13333E-13     4.25508E-05     0.000134744
    20      4.53331E-13     5.66664E-13     5.77474E-05     0.000192491
    21      1.81332E-12     2.37999E-12     7.69966E-05     0.000269488
    22      6.34663E-12     8.72662E-12     0.000101058     0.000370546
    23      1.99466E-11     2.86732E-11     0.000130781     0.000501327
    24      5.73463E-11     8.60195E-11     0.000167109     0.000668436
    25      1.52924E-10     2.38943E-10     0.000211085     0.000879521
    26      3.82309E-10     6.21252E-10     0.000263856     0.00114338
    27      9.03639E-10     1.52489E-09     0.000326679     0.00147006
    28      2.03319E-09     3.55808E-09     0.000400925     0.00187098
    29      4.37918E-09     7.93726E-09     0.000488082     0.00235906
    30      9.07115E-09     1.70084E-08     0.000589766     0.00294883
    31      1.81423E-08     3.51507E-08     0.000707719     0.00365655
    32      3.51507E-08     7.03014E-08     0.000843819     0.00450037
    33      6.6166E-08      1.36467E-07     0.00100008      0.00550045
    34      1.21304E-07     2.57772E-07     0.00117867      0.00667912
    35      2.17071E-07     4.74843E-07     0.00138189      0.008061
    36      3.79874E-07     8.54717E-07     0.0016122       0.0096732
    37      6.51213E-07     1.50593E-06     0.00187223      0.0115454
    38      1.09522E-06     2.60115E-06     0.00216477      0.0137102
    39      1.8095E-06      4.41065E-06     0.00249276      0.016203
    40      2.94043E-06     7.35108E-06     0.00285935      0.0190623
    41      4.70469E-06     1.20558E-05     0.00326783      0.0223301
    42      7.41894E-06     1.94747E-05     0.00372169      0.0260518
    43      1.15406E-05     3.10153E-05     0.00422462      0.0302765
    44      1.7723E-05      4.87383E-05     0.00478049      0.035057
    45      2.68901E-05     7.56284E-05     0.00539338      0.0404503
    46      4.03351E-05     0.000115964     0.00606755      0.0465179
    47      5.98522E-05     0.000175816     0.00680749      0.0533254
    48      8.79079E-05     0.000263724     0.00761791      0.0609433
    49      0.000127866     0.00039159      0.00850371      0.069447
    50      0.000184277     0.000575867     0.00947005      0.078917
    51      0.000263253     0.00083912      0.0105223       0.0894393
    52      0.000372942     0.00121206      0.011666        0.101105
    53      0.000524135     0.0017362       0.0129071       0.114012
    54      0.000731031     0.00246723      0.0142515       0.128264
    55      0.0010122       0.00347943      0.0157058       0.14397
    56      0.00139177      0.0048712       0.0172764       0.161246
    57      0.00190095      0.00677215      0.0189701       0.180216
    58      0.00257987      0.00935202      0.0207942       0.20101
    59      0.00347982      0.0128318       0.0227559       0.223766
    60      0.00466612      0.017498        0.0248629       0.248629
    61      0.0062215       0.0237195       0.0271232       0.275752
    62      0.00825025      0.0319697       0.0295449       0.305297
    63      0.0108833       0.042853        0.0321366       0.337434
    64      0.0142843       0.0571373       0.0349069       0.372341
    65      0.0186571       0.0757944       0.0378652       0.410206
    66      0.0242542       0.100049        0.0410206       0.451227
    67      0.0313878       0.131436        0.0443829       0.495609
    68      0.040442        0.171878        0.0479622       0.543572
    69      0.0518878       0.223766        0.0517687       0.59534
    70      0.0663011       0.290067        0.0558132       0.651154
    71      0.0843832       0.374451        0.0601065       0.71126
    72      0.106986        0.481437        0.06466         0.77592
    73      0.13514         0.616577        0.0694854       0.845405
    74      0.17009         0.786667        0.0745946       0.92
    75      0.213333        1               0.08            1




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